INTRODUCTION

The mathematical difficulties in deriving solutions for growing magnetic fields in spherical geometries have long puzzled dynamo theoreticians. In contrast to the solutions of the kinematic dynamo problem found by Roberts (1970, 1972) and others in the case of periodic velocity fields in infinitely extended electrically conducting fluids, dynamo action often seems to disappear as soon as insulating boundaries are introduced. Motivated by this observation Bullard & Gubbins (1977) have investigated kinematic dynamos in a spherical domain of constant conductivity with insulating exterior for velocity fields with alternating signs as a function of radius. As expected the critical magnetic Reynolds number decreases significantly as the number of sign changes increases and the limit of a periodic velocity field is approached. When the radial velocity component does not change sign, a dynamo solution was not obtained unless an outer shellular region of finite conductivity was introduced.